Although when the word ‘Matrix’ is pronounced, the first image that comes to one’s mind could be the slow-motion action scenes from the American science fiction series of action movies ‘The Matrix’, but as far as mathematical studies and the competitive preparation is considered, a Matrix (whose plural is matrices) is a rectangular array of numbers, symbols, or expressions, arranged in horizontal rows and vertical columns. As matrices can be added, multiplied, transposed, inversed, and decomposed in a number of ways, hence the matrix theory is used to solve the linear equations, making them an important concept in linear algebra, which is, in turn, an essential part of quantitative aptitude section of almost all competitive exams in SSC and Railways category. Many times, one may find the matrix analogy and related questions in the reasoning and data interpretation section too.
Invariably, Matrix related questions are asked in almost every SSC and Railway related competitive exams, be it SSC CGL, SSC CHSL, SSC MTS, SSC CPO, SSC Steno, SSC Constable, SSC JE, HSSC Patwari, HSSC Canal Patwari, HSSC Sachiv, HSSC Clerk, Delhi Police, RRB Group D, RRB JE, RRB NTPC, RRB ALP or any other related competition in government sector in India.
Here are some Matrix notes along with Matrix tricks to ensure that you are fully prepared for such questions in the exam. Prepare with BYJU'S Exam Prep to also get access to numerous Matrix questions and Matrix practice set.
It is important to ensure that you are clear about the Matrix basics and memorise the Matrix formulas before the exam. Solve various Matrix quiz and Matrix online test to master the topic.
Important Matrix Topics for SSC Exams
Topic | Explanation |
Rows | Horizontal lines in a matrix. |
Columns | Vertical lines in a matrix. |
Dimensions of a Matrix | A matrix with m-rows and n-columns is called an m-by-n matrix (written as mxn), and m and n are called its dimensions. |
Element | An individual item in a matrix. |
Matrix Notation | A matrix is shown by a capital letter (such as A, or B), each element is shown by a lower-case letter with a subscript of row and column, example, A = [ai, j] |
Row Vector/ Row Matrix | A matrix with a single row |
Column Matrix | A matrix with a single column |
Square Matrix | A matrix which has the same number of rows and columns |
Null Matrix | A matrix with all elements as zero |
Diagonal Matrix | A square matrix with each of the non-diagonal elements as zero |
Identity Matrix | A diagonal matrix, all of the diagonal elements of which are equal to 1, the rest being equal to 0, denoted by [I] |
Scalar Matrix | Diagonal matrix with non-zero elements are equal and scalar. |
Upper Triangular Matrix | A square matrix whose elements below the leading diagonal are zero. |
Lower Triangular Matrix | A square matrix whose elements above the leading diagonal are zero. |
Addition | Add each element in the first matrix to the corresponding element in the second matrix. |
Subtraction | subtract each element in the second matrix from the corresponding element in the first matrix. |
Scalar Multiplication | Directly multiply each element of the matrix with the scalar multiplier (constant term) |
Matrix Multiplication | If A is an nxm matrix, and B is an mxp matrix, the result AB of their multiplication is an nxp matrix. Multiplication is possible only if the number of columns m in A is equal to the number of rows m in B. |
Transpose of Matrix | The transpose of a matrix is found by exchanging rows for columns that is, the transpose of matrix A is AT = [aj, i] where i is the row number of matrix A and j is the column number of matrix, A = [ai, j] |
Determinant of Matrix | Denoted by det(A) or |A|, if A is an n×n matrix the determinant is given by: Where the coefficients αij are given by the relation: where βij is the determinant of the (n-1) × (n-1) matrix that is obtained by deleting row i and column j. This coefficient αij is the cofactor of aij. |
Inverse of Matrix | Defined for the non-singular matrix, inverse is a matrix which if multiplied by the original matrix will yield the identity matrix, denoted by A-1,, where adjoint is the transpose of the matrix formed by taking the cofactors of each element to form a matrix. |
Tips to Solve/ Prepare Matrix Questions for SSC Exams
- Go on solving the numerical problems, rather than mugging the Matrix theory
- Keep the Matrix and related properties and thumb-rules handy. This will help to lower the attempt time and ensure the answer's accuracy.
- For the questions related to finding the determinant and inverse of matrices, do not jump the steps.
Importance of Matrix in Quantitative and Reasoning section of SSC and Railway Exams
- In almost every exam, a candidate could find the Matrix related questions.
- If practised properly, these questions may save the overall time to attempt the paper.
- Remembering the Matrix properties, chances of wrong replies to Matrix questions are negligible.
- Other forms of linear algebra questions, such as age, fractions, non-verbal reasoning, etc could be solved in an easier way by converting them to Matrix forms.
Most Recommended Books for Matrix (Linear Algebra)
Check the best books to ensure that you understand and practice the Matrix topics and questions in the Linear Algebra section.
S.No. | Books | Author |
1. | Verbal & Non-Verbal Reasoning | R. S. Aggarwal |
2. | Verbal & Non-Verbal Reasoning (Hindi) | Kiran Publication |
3. | Fast Track Objective Arithmetic | Arihant Publication |
4. | For Notes, Study Material and Online Quiz (thousands of questions to practice are available) | Gradeup |
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Frequently Asked Questions about Matrix questions
Q1: Can there be a matrix with 0x0? If yes, then how is it represented.
It could be just an empty matrix, like this: [ ] However, such a matrix could not contain any information.
Q2: What is the purpose of such an arrangement of numbers in a matrix?
The arrangement enables the storage of data in such a way that one can easily perform various algebraic operations on the entire data set.
Q3: How to multiply two 3x3 matrices?
Q4: How to find the determinant of a 3x3 matrix?
Q5: How to find the inverse of a 2x2 matrix?
Q6: What is the determinant of matrix ?
As per the definition of determinant, it is {det = ad-bc}
Q7: Is this a diagonal matrix ?
Yes, it is. A diagonal matrix doesn't mean that zeros on the leading diagonal are not allowed.
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